IRD Determination G3: Yield to Maturity Method for Bonds (worked example)

[Snoopy]

Below is the first table, exactly as it appears in Determination G3.

Period Ending	Principal Outstanding	Income in Respect of Period	Payments Received at End of Period
15-05-1987	$1,012,500	$28,815	$70,000
15-11-1987	$971,315	$78,826	$70,000
15-05-1988	$980,141	$79,542	$70,000
15-11-1988	$989,638	$80,317	$1,070,000
Total		$267,500	$1,280,000

The table is modelled using six month timing blocks. After each block 'times through', a $70k interest payment is made. But because the bond acquisition was made half way through the first period, not all of that first $70k interest payment will accrue to our bond buyer, and now bond owner.

I had assumed (during my first attempt) the purchase price of $1,012,500 did not extinguish the requirement for the bond buyer to refund the seller of the bond their interest due ($45,452.05). However, I now believe it does. I can model this by not recording the bond purchase price as $1,012,500, but rather as: $1,012,500-$45,452=$967,048




The first period, ending 15-05-1987, represents 64 days (refer post 2) of a half year period over which $70k of interest would be paid to the bondholder - if they had held those bonds for 6 months. But since 'our bondholder' only held those bonds for 64days, their share of that interest would be just: $70,000 x [64/(365x0.5)]= $24,547.95. That leaves the interest balance ($70,000-$24547.95= $45,452.05) to be refunded to the previous bondholder. (In practice this refund was not a retrospective transaction, as the interest accrued is being priced into the bond in the 'market price' already, on a daily basis).

The total capital gain only (all taxable of course) on these bonds held by our investor over the whole investment period covered in the table was therefore:
($1,280,000 - 4x$70.000) - $967,048 = +$32,952
This represents a capital gain of $32,952/[64+1.5x365]days = $53.89 per day

For income tax purposes, we must add to the 'share of interest' of $24,547.95, the portion of 'extra capital' (capital gain) our bondholder will get back that has been apportioned to this period: 64x$53.89=$3,448.96. So total taxable earnings (income and capital gain) for the initial period now add to: $24,547.95+$3,448.96=$27,996.91





Now we move on to the three six monthly income periods. Interest income for each of those is $70,000. But once again there is a 'capital adjustment' to be made for each period of: $53.89 x (365/2)= $9,834.93. So taxable earnings for the full six month period add to: $70,000+$9,834.93= $79,834.93

As previously discussed (post 1), all of the 'capital adjustments' change the book value of the capital of the bond remaining for income tax purposes (column 2 in the above table). Using my 'first principles' analysis, I will now rewrite the reallocated income table that I have replicated above, as below:

Period Ending	Principal Outstanding (for tax accounting purposes) (1)	Adjusted Gross Income - including capital gains - in Respect of Period	Already Income Incorporated Taxable Capital Gain	Payments Received by End of Period
Day of Opening Investment (2)	$967,048
15-05-1987	$963,599	$27,997	$3,449	$70,000
15-11-1987	$953,764	$79,835	$9,835	$70,000
15-05-1988	$943,929	$79,835	$9,835	$70,000
15-11-1988	$934,094	$79,835	$9,835	$1,070,000
After Investment matures	.$0
Total		$267,502	$32,994	$1,280,000

Notes

1/ Capital adjustments period to period are as follows:
@15-05-1987: $967,048-$3,449=$963,599
@15-11-1987: $963,599-$9,835=$953,764
@15-05-1988: $953,764-$9,835=$943,929
@15-11-1988: $943,929-$9,835= $934,094

2/ Transfer required of income paid to 'our investor' that belonged to the Previous Bond Owner:$ $70,000-$24,548=$45,452. Therefore, the equivalent starting capital was: $1,012,500-$45,452 = $967,048


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The above table looks pretty close to the one published in the IRD Determination D3 now. The 'adjusted income' is $2 more than the reference table. But that $2 is simply a 'rounding error'. If we add back to the 'principal outstanding' my pre-investment 'interest owed' adjustment of $45,452 we get: $934,094+ $45,452 = $979,546. That is about 10 grand smaller than the $989,638 declared in the reference table.

As Snow Leopard has noted (post 12), I have calculated a 'linear income over the entire period of the loan', which is not what the authors of the reference table have done. But it is in accord with IRD Determination G1A which states:

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G1A 4 December 1989

2. This determination requires that income derived or expenditure incurred in respect of a period shall be apportioned on a straight line basis among the income years in which the period falls, according to the number of days in the period calculated on either a 365 or a 360 day basis.

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A 'straight line basis' means 'linear income' in my books.

SNOOPY